Question

Find Maclaurin series for the function f(x)=Ln(e+x^2) and state whether the series converges to the function

Answer 1

Show me your best guess and explain what you do/don't understand so I don't waste time explaining things you already know.

Answer 2

I set for f(x) =ln(e+x^2). I know I need to f''(x)...etc but I don't understand how to do that with the e!

Answer 3

e's a constant right? So when you take the derivative using the chain rule you will find that the derivative of e is 0. So:

\[f'(x)=\frac{ 1 }{ e+x^2 }*(0+2x)\]

I tried to leave this unsimplified so you can see that the first part is just the normal, regular derivative of the natural logarithm and then (0+2x) is the derivative of (e+x^2).